Aperiodic geometry design for DOA estimation of broadband sources using compressive sensing

Abstract

• The coordinate system has been added as Fig. 1 • Details of the theoretical work have been added. (In the paragraph after (11)) • Several typos have been fixed (details are contained in the individual replies to the reviewers.) • Captions for Figs. 5 and 7 have been added. • The term “probability of resolution” has been defined and details added. Antenna arrays used in Compressive Sensing (CS) based algorithms are generated randomly to minimize mutual coherence. This scheme, although good for compressive sensing, suffers from practical limitations. Random sampling of antenna aperture is impractical. Rectangular arrays, although uniform, suffer from poor performance when used in CS algorithms. It is particularly ill suited to algorithms designed to estimate DOA of broadband sources, because of the introduction of grating lobes. Aperiodic arrays offer some advantages in the CS scenario. The aperiodic geometries based on Penrose and Danzer tiling are inherently sparse as they utilize a fewer number of sensors as compared to the regular geometries. Based on minimization of mutual coherence, this paper develops a novel optimization scheme, that can generate sparse array geometries offering improved performance for CS algorithms. This paper demonstrates that it is possible to design aperiodic arrays that perform much better than rectangular arrays by using a simple disturbance optimization scheme, that can be applied to other aperiodic geometries as well. A greedy MMV based compressive sensing algorithm, SOMP, is used to evaluate the performance of a number of geometries. Two geometries have been identified that perform better than all other geometries studied, including the random-sampling based geometries.